# Higher Order Nonclassicality from Nonlinear Coherent States for Models with Quadratic Spectrum

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## Abstract

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## 1. Introduction

## 2. Nonlinear Coherent and Squeezed States

## 3. Nonclassicality via Entanglement

## 4. Nonclassical Models

#### 4.1. Linear versus Quadratic Spectrum

#### 4.2. Linear Plus Quadratic Spectrum

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Dispersion in position ${(\Delta x)}^{2}$, momentum ${(\Delta p)}^{2}$ and product of dispersions $\Delta (z,0)={(\Delta x)}^{2}{(\Delta p)}^{2}$ for the usual (solid lines) and quadratic (dashed lines) coherent states of the harmonic oscillator.

**Figure 2.**Density probabilities ${\left|\psi (z,f)\right|}^{2}$ for usual (

**left**) versus the quadratic (

**right**) coherent states of the harmonic oscillator.

**Figure 3.**Linear entropy for squeezed states of harmonic oscillator (dashed lines) versus quadratic spectrum (solid lines).

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**MDPI and ACS Style**

Hertz, A.; Dey, S.; Hussin, V.; Eleuch, H.
Higher Order Nonclassicality from Nonlinear Coherent States for Models with Quadratic Spectrum. *Symmetry* **2016**, *8*, 36.
https://doi.org/10.3390/sym8050036

**AMA Style**

Hertz A, Dey S, Hussin V, Eleuch H.
Higher Order Nonclassicality from Nonlinear Coherent States for Models with Quadratic Spectrum. *Symmetry*. 2016; 8(5):36.
https://doi.org/10.3390/sym8050036

**Chicago/Turabian Style**

Hertz, Anaelle, Sanjib Dey, Véronique Hussin, and Hichem Eleuch.
2016. "Higher Order Nonclassicality from Nonlinear Coherent States for Models with Quadratic Spectrum" *Symmetry* 8, no. 5: 36.
https://doi.org/10.3390/sym8050036